Vortex pairs on surfaces
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2009
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A pair of infinitesimally close opposite vortices moving on a curved surface moves along a geodesic, according to a conjecture by Kimura. We outline a proof. Numerical simulations are presented for a pair of opposite vortices at a close but nonzero distance on a surface of revolution, the catenoid. We conjecture that the vortex pair system on a triaxial ellipsoid is a KAM perturbation of Jacobi's geodesic problem. We outline some preliminary calculations required for this study. Finding the surfaces for which the vortex pair system is integrable is in order.
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